十字轴机械加工工艺规程及工艺钻4-φ6通孔装备夹具设计【含CAD图纸】
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夹具定位规划中完整性评估和修订CAM实验室,机械工程学系,伍斯特理工学院研究院,100路,伍斯特,硕士01609,美国2004年9月14日收稿;2004年11月9日修订;2004年11月10日发表摘 要几何约束是夹具设计中最重要的考虑因素之一。确定位置的解析拟订已发达。然而,如何分析和修改在实际夹具设计实践过程中的一个非确定性的定位计划尚未深入研究。在本文中,提出了一种方法来描述在限制约束下的重点夹具系统的几何约束状态。一种限制约束下状态,如果它存在,可以识别给定定位计划。可以自动识别工件的所有限制约束下约束状态的提案。这有助于改善逆差定位计划,并为修订提供指引,以最终实现确定性的定位。 关键词:夹具设计;几何约束;确定性定位;限制约束;过约束1.介绍夹具是用于制造工业进行工件牢固定位的一种机制。在零件加工过程中规划一个关键的第一步,夹具设计需要,以确保定位精度和三维工件的精度。 3-2-1原则,在一般情况下,是最广泛使用的指导原则发展的位置计划。 V型块和销孔定位原则也常用。一个加工夹具定位方案必须满足一些要求。最基本的要求是,必须提供工件确定的位置。这种观点指出,定位计划生产的确定位置,工件不能移动,而至少有一个定位不会失去联系。这一直是夹具设计的最根本的准则之一,许多研究人员关于几何约束状态的研究表明,工件在任何定位计划分为以下三个类别:1、良好的约束(确定性):工件在一个独特的位置进行配合,工件表面与6个定位器取得联系。 2、限制约束:不完全约束工件的自由度。 3、过约束:工件自由度超过6定位的制约。 在1985年,浅田1提出了满秩为准则雅可比矩阵的约束方程,基于分析形成了调研后,确定定位。周等2在1989年制定了在确定性定位问题上使用螺旋理论。结果表明,定位矩阵的定位需要压力满秩达到确定的位置。该方法的确定通过无数的研究。王等3考虑定位工件的接触的影响,而采用点接触面积。他们介绍了接触矩阵,并指出,两个接触的机构不应该有平等的,但在接触点曲率相反。卡尔森4认为,可能没有足够的应用,如一些不是非棱柱的表面或相对误差近似的非小线性。他提出一个二阶泰勒展开,其中也考虑到定位误差相互作用。马林和费雷拉5应用周对3-2-1的位置拟订,制定若干按照规则的规划。尽管众多的位置上的确定分析研究很少注意非确定性分析的位置。在浅田的拟定方案中,他们假设工件夹具元件和点之间的联络无阻力。理想的位置q*,而应放置工件表面和分片,可微函数是gi(见图1)。 表面函数定义为:gi(q*)=0是确定的,应该有一个独一无二的解决方案为下列所有定位方程组。gi(q)=0,i=1,2,.,n (1)其中n是定位器的位置与方向,代表了工件的定位和方向。只有考虑到目标位置q*附近在处:浅田表明 (2) hi是几何函数的雅可比矩阵,矩阵式所示(3)。确定定位如果雅可比矩阵满秩,可满足要求。 (2)只有q=q*一个解决办法 (3)在1个3-2-1定位计划中,一个约束方程的雅可比矩阵的满秩的约束状态如表1所示。如果定位是小于6,工件是限制约束的,即存在至少有一个工件自由定位议案不受限制的。如果矩阵满秩,但定位大于6定位,工件是过约束,这表明存在至少一个定位等;而几何约束工件被删除不影响的状态。找出一个模型除了3-2-1,可以建立基准框架提取等效的定位点。胡等6已经发展出一种系统的方法,对这个用途。因此,这则能适用于所有的定位方案。图1 .夹具系统模型。表1 等级 数量的定位 地位 6 Over-constrained康等7遵循这些方法和他们实施制定的几何约束分析模块其自动化的计算机辅助夹具设计的核查制度。他们的CAFDV系统可以计算出雅可比矩阵和它的排名来确定定位的完整性。它也可以分析工件的位移和灵敏度定位错误。熊等人8提出的等级检查方法的定位矩阵WL(见附件)。他们还介绍了左/右边的定位矩阵广义逆理论,分析了工件的几何误差。结果表明,定位及发展方向误差X和位置误差r的工件定位相关如下: Under-constrained:X=WLr, (4)Well-constrained :X=(WTLWL)-1WLTr, (5)Over-constrained:X=WLT(WTLWL)-1r+(I6*6-WLT(WTLWL)-1WL), (6)是任意一个向量。 他们还介绍了从这些矩阵的几个指标,评价定位配置,其次是通过约束非线性规划的优化。然而,他们的研究分析,不涉及非确定性定位的修订。目前,还没有就如何处理与提供确定的位置的夹具设计系统的研究。 2.定位完整性评价如果不确定性的位置达到夹具系统设计的要求,设计师知道约束状态是什么,以如何改善设计是非常重要的条件。如果夹具系统是过度约束,是理想定位需要的不必要的信息。而下约束时,所有有关知识约束工件的议案,可以引导设计师选择额外的定位或使得修改定位计划更有效。的总体战略定位计划表征几何约束的状态描述图 2。在本文中,定位矩阵秩的几何约束的施加评价状态(见附件为获得的定位矩阵)。确定需要六个定位器定位提供矩阵的满秩定位WL:如图3所示,在给定的定位器数量n,定位法向量ai,bi,ci和定位的位置xi,yi,zi每一个定位器,i=1,2,.,n,n*6定位矩阵可以确定如下: (7)当等级(WL)=6,n=6时,是工件良好约束。 当等级(WL)=6,n6时;是工件过约束。这意味着(n-6)有不必要的定位在定位方案上。工件将不存在限制(n-6)定位器。这种状态的数学表示方法,那就是(n-6)在定位向量矩阵,可表示为线性组合的其他六行向量。 图2 几何约束状态描述 图3一个简化的定位方案。定位方案,提供了确定性的位置。发达国家的算法使用下列方法确定不必要的定位:1、找到所有的(n-6)组合定位的。2、为每个组合,从(n-6)定位器确定定位方案。3、重新计算矩阵秩的定位为左六个定位器。4、如果等级不变,被删除的(n-6)定位器是负责过约束状态。这种方法可能会产生多种解决方案,并要求设计师来决定哪一套不必要的定位应该被删除以最佳定位性能。 当等级(WL)6,工件的限制约束。参考文献1 Asada H, By AB.。自动重构夹具的柔性装配夹具的运动学分析。 IEEE J机器人autom1985; RA-1:86-93。2 zhou YC,Chandru V,Barash MM。加工装置的自动配置的数学方法分析和综合。反ASME J英工业1989;111:299-306。3 Wang MY, Liu T, Pelinescu DM.。夹具运动学分析的基础上充分接触刚体模型。 J制造业科学与工程2003;125:316-24。4 Carlson JS。刚性零件的装夹和定位计划的二次灵敏度分析“。 ASME J制造业2001年科学与工程;123(3):462-72。5 Marin R, Ferreira P.确定性3-2-1定位计划的运动学分析和综合加工装置。 ASME J制造业科学与工程2001年;123:708-19。6 Hu W.设置规划和公差分析。博士论文中,伍斯特理工学院;2001年。7 Kang Y, Rong Y, Yang J, Ma W.计算机辅助夹具设计验证。大会Autom2002;22:350-9。8 Rong KY, Huang SH, Hou Z.先进的计算机辅助夹具设计。波士顿:爱思唯尔;2005年。辽宁工程技术大学课 程 设 计题 目:十字轴机械加工工艺规程及工艺装备设计班级:机械工程及自动化 姓名: 指导教师: 完成日期: 课程设计任务书一、设计题目 十字轴机械加工工艺规程及工艺装备设计二、原始资料(1) 被加工零件的零件图 1张(2) 生产类型:大批生产三、上交材料(1) 被加工工件的零件图 1张(2) 工件的毛坯图 1张(3) 机械加工工艺过程卡片 1张(4) 与所设计夹具对应那道工序的工序卡片 1张(5) 夹具装配图 1张(6) 夹具体图 1张(7) 课程设计说明书(60008000字) 1份说明书主要包括以下内容(章节)目录 摘要(中外文对照的,各占一页)零件工艺性分析机械加工工艺规程设计 指定工序的专用机床夹具设计 方案综合评价与结论体会与展望参考文献 列出参考文献(包括书、期刊、报告等,10条以上)课程设计说明书一律用A4纸、纵向打印.四、进度安排(参考)(1) 熟悉零件,画零件图 2天 (2) 选择工艺方案,确定工艺路线,填写工艺过程综合卡片 5天(3) 工艺装备设计(画夹具装配图及夹具体图) 9天(4) 编写说明书 3天(5) 准备及答辩 2天五、指导教师评语成 绩: 指导教师日期成绩评定采用五级分制,即优秀、良好、中等、及格和不及格。优秀:设计方案合理并新颖,设计说明书及设计图纸规范、内容丰富。在设计过程中勤奋好学、有创新思想;良好:设计方案合理,设计说明书及设计图纸比较规范、内容比较丰富。在设计过程中勤奋好学、有创新思想;中等:设计方案一般,设计说明书及设计图纸欠规范、内容一般。在设计过程中比较勤奋、创新思想不明显; 及格:设计方案不完善,存在一些小错误,说明书及设计图纸欠规范、内容一般。在设计过程中勤奋精神不够: 不及格:设计方案有严重错误,设计说明书及设计图纸不规范、内容浅薄。在设计过程中勤奋好学精神不够。摘要这次设计的是十字轴机械加工工艺规程及工艺装备设计,包括零件图、毛坯图、装配图各一张,机械加工工艺过程卡片和与工序卡片各一张。首先我们要熟悉零件和了解其作用,它位于车床变速机构中,主要起换档作用。然后,根据零件的性质和零件图上各端面的粗糙度确定毛坯的尺寸和械加工余量。最后拟定拨差的工艺路线图,制定该工件的夹紧方案,画出夹具装配图。就我个人而言,我希望能通过这次课程设计,了解并认识一般机器零件的生产工艺过程,巩固和加深已学过的技术基础课和专业课的知识,理论联系实际,从中锻炼自己分析问题、解决问题的能力,为今后的工作打下一个良好的基础,并且为后续课程的学习打好基础。AbstractThis time I design the lathes of the shift forks CA6140(831005), including that the part pursuing , the blank pursues , assembling pursues , the machine work procedure card the working procedure card every sheet .We should know the part very well and know its effect first , it is worked in the organization which is used for change the speed in a lathe, and the mainly role of the part is alter the speed. Then, we design the dimension of the blank and instrument process a margin of the part according to part character and the harshness of each face .Finally, I design the handicrafts route picture of the shift forks, work out the fastening motion scheme being workpieces turn , draw up clamp assembling picture. As far as my individual be concerned, I want to knowing the general productive technology of machine part , consolidating and deepening the knowledge of basic course and specialized course what I have already learned , integrates theory with practice, and improve the ability to solve problems, whats more , striking the basis for the future work and the following courses studying .目录一、零件的工艺分析1二.机械加工工艺设计21、确定生产类型22、确定毛坯22.1、确定毛坯种类:22.2、确定锻件加工余量及形状:2三、工艺规程设计43.1选择定位基准:43.2制定工艺路线:43.3表面加工方法的确定53.4加工阶段的划分53.5工序顺序的安排53.6确定工艺路线6四.机械加工余量、工序尺寸及公差的确定74.1 钻铰8丝孔 的工序尺寸74.1.1.钻5丝孔,以25轴线为基准。74.2.2 钻孔工步74.3时间定额的计算:74.4 其它时间计算8五、夹具设计95.1夹具选择95.1.1问题的提出95.1.2夹具设计105.2、定位误差分析105.3、夹具设计及操作的简要说明11六.参考文献12十字轴机械加工工艺规程及工艺装备设计:序言机械制造工艺学课程设计是我们学完了大学的全部基础课、技术基础课以及大部分专业课之后进行的.这是我们在进行毕业设计之前对所学各课程的一次深入的综合性的总复习,也是一次理论联系实际的训练,因此,它在我们四年的大学生活中占有重要的地位。就我个人而言,我希望能通过这次课程设计,了解并认识一般机器零件的生产工艺过程,巩固和加深已学过的技术基础课和专业课的知识,理论联系实际,对自己未来将从事的工作进行一次适应性训练,从中锻炼自己分析问题、解决问题的能力,为今后的工作打下一个良好的基础,并且为后续课程的学习大好基础。由于能力所限,设计尚有许多不足之处,恳请各位老师给予指导。一、零件的工艺分析 零件的材料为 20GrMoTi, 需要模锻, 模锻性能优良, 工艺较复杂 ,但尺寸精确,加工余量少,为此以下是十字轴需要加工的表面以及加工表面之间的位置要求:1、 四处25外圆及四个8、4的内孔、2、右端面5060内孔及M8丝孔。3、25外圆的同轴度为0.007,位置度为0.02,两端的对称度均为0.05.由上面分析可知,可以先上四爪卡盘粗车,然后上弯板采用专用夹具压紧、找正进行加工,并且保证形位公差精度要求。 并且此 零件没有复杂的加工曲面,所以根据上述技术要求采用常规的加工工艺均可保证。二.机械加工工艺设计1、确定生产类型 已知此 十字轴零件的生产纲领为5000件/年,零件的质量是083Kg/个,查机械制造工艺设计简明手册第2页表1.1-2,可确定该拨叉生产类型为中批生产,所以初步确定工艺安排为:加工过程划分阶段;工序适当集中;加工设备以通用设备为主,大量采用专用工装。2、确定毛坯2.1、确定毛坯种类:零件结构又比较简单,生产类型为中批生产,故选择锻模锻造毛坯。查机械制造工艺设计简明手册第41页表2.2-5,选用铸 锻件尺寸公差等级为CT-10。2.2、确定锻件加工余量及形状:查机械制造工艺设计简明手册第41页表2.2-5,选用加工余量为MA-H级,并查表2.2-4确定各个加工面的锻件机械加工余量, 如下表所示:简 图加工面代号基本尺寸加工余量等级加工余量说明a25H2双侧加工b25H 双侧加工c25H5双侧加工d25H5双侧加工 三、工艺规程设计3.1选择定位基准:1 粗基准的选择: 作为粗基准的表面应平整,没有飞边、毛刺或其他表面缺欠。该工件选择25外圆面和左端面作为粗基准。采用左端面作粗基准加工右端面,可以为后续工序准备好精基准 2 精基准的选择:考虑要保证零件的加工精度和装夹准确方便,依据“基准重合”原则和“基准统一”原则,以粗加工后25的轴线为主要的定位精基准,采用小弯板为辅助的定位精基准。3.2制定工艺路线:生产过程是指将原材料转变为成品的全过程。它包括原材料的准备、运输和保存,生产的准备,毛坯的制造,毛坯经过加工、热处理而成为零件,零件、部件经装配成为产品,机械的质量检查及其运行试验、调试,机械的油漆与包装等。 工艺过程是指在生产过程中,通过改变生产对象的形状、相互位置和性质等,使其成为成品或半成品的过程。机械产品的工艺过程又可分为铸造、锻造、冲压、焊接、机械加工、热处理、装配、涂装等工艺过程。其中与原材料变为成品直接有关的过程,称为直接生产过程,是生产过程的主要部分。而与原材料变为产品间接有关的过程,如生产准备、运输、保管、机床与工艺装备的维修等,称为辅助生由于零件加工表面的多样性、生产设备和加工手段的加工范围的局限性、零件精度要求及产量的不同,通常零件的加工过程是由若干个顺次排列的工序组成的。工序是加工过程的基本组成单元。每一个工序又可分为一个或若干个安装、工位、工步或走刀。毛坯依次通过这些工序而变成零件。 1. 工序 工序是一个或一组工人,在相同的工作地对同一个或同时对几个工件连续完成的那一部分工艺过程。 工序是组成工艺过程的基本单元,也是生产计划、成本核算的基本单元。一个零件的加工过程需要包括哪些工序,由被加工零件的复杂程度、加工精度要求及其产量等因素决定3.3表面加工方法的确定根据零件的几何形状、尺寸精度及位置精度等技术要求,以及加工方法所能达到的经济精度,在生产纲领已确定的情况下,可以考虑采用万能性机床配以专用工卡具,并尽量使工序集中来提高生产率。除此之外,还应当考虑经济效果,以便使生产成本尽量下降。查机械制造课程设计指导书10页表1-6、1-7、1-8, 选择零件的加工方法及工艺路线方案如下: 十字轴零件加工方案加工项目尺寸公差等级粗糙度加工方案备注25外圆 IT8 6.3粗车-半精车表1-6左右端面 IT1012.5粗 车表1-625外圆 IT86.3粗车-半精车表1-8上下端面IT1012.5粗 车表1-7 23、孔IT93.2钻-铰表1-7、内螺纹M8 IT63.2攻螺纹表1-10 4孔 IT1212.5钻表1-78孔 IT1212.5钻 表1-73.4加工阶段的划分在粗加工阶段。首先将精基准准备好,使后续工序都可以采用精基准定位加工,保证其他加工表面的精度要求;首先25圆面作为粗基准粗车右端面及25,然后以此圆轴线及端面为精基准加工其他面和孔。在采用小弯板加工 另一部分,以保证其形位公差之要求。选用工序集中原则安排十字轴的加工工序。该零件的生产类型为大批生产,可以采用万能型机床配以专用工、夹具,以提高生产率;而且运用工序集中原则使工件的装夹次数少,不但可以缩短辅助时间,而且由于与一次装夹中加工了许多表面,有利于保证各种加工表面之间的相对位置精度要求。3.5工序顺序的安排机械加工工序(1)遵循“先基准后其他”原则,首先加工基准25外圆轴线及端面 。(2)遵循“先粗后精”原则,先安排粗加工工序,后安排精加工工序。(3)遵循“先主后次”原则,先加工主要表面(4)遵循“先面后孔”原则,先加工外圆面、端面,再加工孔,确定工艺路3.6确定工艺路线工序号工序名称机床装备刀具量具1粗-半精车25 两处 车床车刀游标卡尺2粗车左右端面车床车刀游标卡尺3粗-半精车25 两处车床车刀游标卡尺4粗车上下端面车床车刀游标卡尺5钻铰8丝孔2360内孔,车床钻头铰刀塞规.卡尺6攻螺纹M8车床丝锥塞规.卡尺7钻4、8孔钻床钻头锥度铰刀游标卡尺8中检 游标卡尺10热处理淬火机等12终检塞规、百分表、卡尺等加工设备和工艺设备1 机床的选择:采用CA6140普通车床、钻床。磨床 2 选择夹具:该零件的生产纲领为大批生产,所以采用专用夹具。3选择量具:采用塞规.双用游标卡尺。四.机械加工余量、工序尺寸及公差的确定4.1 钻铰8丝孔 的工序尺寸由表2-28课查得,精铰余量Z=0.2mm,加工等级为IT8,公差为0.015钻孔余量为Z钻=4.8mm,加工等级为IT12,公差为0.15。钻铰8 孔加工工序的加工余量项目内容精度等级工序尺寸粗糙度工序余量公差8丝孔钻IT127.812.54.80.15铰IT883.20.20.015主轴转速的确定4.1.1.钻5丝孔,以25轴线为基准。刀具:钻头直径为7.8mm的高速钢钻头,丝锥直径为8mm 。机床:CA61404.2.2 钻孔工步背刀吃量p的选择粗加工时根据加工余量和工艺系统刚度确定p=7.8mm。进给量的确定 由表5-22,选取该工步得进量f=0.1mm/r。切削速度的计算 由表5-31,按工件材料为铸铁的条件选取,切削速度v=20m/min选取。由公式n=1000v/d可求得该工序钻头钻速n=1326r/min,参照表4-9所列CA6140得主轴转速,取转速n=1360r/min。再将此转速代入公式v=nd/1000=20.5m/min。4.3时间定额的计算:工序6:钻 8丝孔 钻孔工步根据表5-51,钻孔的基本时间可由公式 求得。,;f=0.1mm/r;n=1360r/min。则该工步的基本时间t=(22+2.4+2)/0.1mm/r x 1360r/min=10.8s 攻丝孔工步 根据表5-41,铰孔基本时间可由公式t=L*i/fn=(LP+l1)*i/fn, LP=(D-d)/2*tankr, kr=15,l1=1mm,f=1mm/r,n=195r/min则该工步的基本时间t=20s。辅助时间的计算tf辅助时间tf基本时间t之间的关系为tf=(0.15-0.2)t钻孔辅助时间tf=0.210.8=2.2s铰孔辅助时间tf=0.220=4s4.4 其它时间计算除了作业时间以外,每道工序的单件时间还包括布置工作时间、休息与生理需要时间和准备与终结时间。由于该设计的生产类型为大批量生产,分摊到每个工件上的准备与终结时间甚微,可忽略不计。布置工作地时间tb是作业时间的2%-7%,休息与生理时间tx是作业时间的2%-4%,本设计均取3%,则工序的其他时间(tb +tx)可按关系式(3%+3%)(tf+t)计算。工序6的其他时间:tb +tx=6%(10.8s+20s+4s)=2s单件计算时间td=2s+10.8s+20s+4s=36.8s。 五、夹具设计为了提高劳动生产率,保证加工质量,降低劳动强度,需要设计专用夹具。并设计工序7钻6通孔的夹具。本夹具将用于Z525立式钻床,刀具为高速钢麻花钻。5.1夹具选择夹具是一种能够使工件按一定的技术要求准确定位和牢固夹紧的工艺装备,它广泛地运用于机械加工,检测和装配等整个工艺过程中。在现代化的机械和仪器的制造业中,提高加工精度和生产率,降低制造成本,一直都是生产厂家所追求的目标。正确地设计并合理的使用夹具,是保证加工质量和提高生产率,从而降低生产成本的重要技术环节之一。同时也扩大各种机床使用范围必不可少重要手段。5.1.1问题的提出本夹具主要用来钻 6 孔,该孔为通孔,没有技术要求,在本工序加工时还应考虑如何提高劳动生产率,降低劳动强度,而其位置尺寸为自由公差,精度不是主要问题。5.1.2夹具设计1、定位基准选择 由零件图可知,46孔 ,没有技术要求,为使定位误差为零,应该选择轴线为定位基准保证该角度。 为了提高加工效率,现决定采用手动夹紧工件快换装置, 2、切削力及夹紧力计算 刀具:硬质合金麻花钻,d=5.8mm。由实际加工的经验可知,钻削时的主要切削力为钻头的切削方向,即垂直于工作台,查切削手册表2.3,切削力计算公式为: 其中:,d=5.8mm。,与加工材料有关,取0.94;与刀具刃磨形状有关,取1.33;与刀具磨钝标准有关,取1.0,则: 5.2、定位误差分析(1)定位元件尺寸及公差的确定。夹具的主要定位元件为六个定位销,这六个定位销的尺寸与公差规定为与本零件在工作时与其相匹配轴的尺寸与公差相同,。此外,这六定位销共同保证加工孔 , (2)计算钻套中心线与工作台的垂直度误差。钻套外径36与衬套孔25的最大间隙为:则钻套中心与工作台平面的垂直度误差为:0.026-0.005=0.021。(3)计算定位销轴与工作台的平行度误差。定位销轴与夹具体孔的最大间隙为:夹具体孔的长度为14mm,则上述间隙引起的最大平行度误差为:0.034/14,即0.24/100。5.3、夹具设计及操作的简要说明 如前所述,在设计夹具时,应该考虑提高劳动生产率。为此,设计采用了快换装置。拆卸时,松开夹紧螺母12扣,拔下开口垫圈,实现工件的快换。攻螺纹时,松开压紧螺母即可替换可换钻套,进行攻螺纹加工。 十字轴零件图: 六.参考文献 1、赵家奇,机械制造工艺学课程设计指导书(2版),机械工业出版社,2006年.2、曾志新,吕明主编,机械制造技术基础,:武汉理工大学出版社,2001年.3、李益明主编,机械制造工艺设计简明手册,机械工业出版社,1993年.4、肖诗纲主编,切削用量手册,机械工业出版社,1993年.5、金属切削机床夹具设计手册.上海柴油机厂工艺设备研究所编,机械工业出版社,1987年.附表1 机械加工工艺过程综合卡片零件号 材料20GrMoTi 编制机械加工工艺过程综合卡片零件名称 十字轴毛坯重量1.34kg 指导生产类型大批生产毛坯种类锻件审核工序安装(工位)工步工序说明工序简图机床夹具或辅助工具刀具 4 12 钻孔钻6孔,孔深54mm调头夹紧,钻6孔深至通孔 台钻专用夹具麻花钻头 6mm 零件号 材料 20GrMoTi编制机械加工工艺过程综合卡片零件名称十字轴毛坯重量 1.34kg指导生产类型大批生产毛坯种类铸件审核工序安装(工位)工步工序说明工序简图机床夹具或辅助工具刀具 4 34 钻另一端6孔深54mm。调头夹紧,钻6孔深至通孔台钻专用夹具麻花钻头 6mm 2机械加工工艺过程卡片产品型号零件图号产品名称零件名称十字轴共1页第1页材 料 牌 号20CrMoTi毛 坯 种 类模锻毛坯外形尺寸每毛坯件数1每 台 件 数1备 注 工 序 号 工 序 内 容设 备工 艺 装 备工 时夹具刀具名称刀具规格量 具1车25外圆至25.50.0228确保两处108位置度要求普通车床CA6140四抓卡盘YW1 45.游标卡尺3min2 平端面,保证108至1090.03普通车床CA6140小弯板YW145游标卡尺3min3将109一端25.50.0228装入弯板,用压板压紧定位,车另一端面保证对称度车25至25.20.02长29.90.02倒钝普通车床CA6140小弯板YW145游标卡尺3min4车另一端面将25.20.0229.9装入压板孔内用压板压紧,车25至25.20.0229.9保轴颈形位公差的要求普通车床CA6140小弯板YW145游标卡尺3min5松开压板调头,将另一端装入25.2孔内压紧,车25至25.20.0229.9保108的要求松开压板车另外一端至尺寸25.20.02长29.90.02普通车床CA6140小弯板YW145游标卡尺3min6钻车M8丝孔, 2360深4,倒角60普通车床CA6140四爪夹盘钻头游标卡尺、千分尺5min7 钻46孔,钻48深26孔,倒角60台钻钻模钻头卡尺9min8热处理,淬火25四个轴颈上,硬度保证HRC58-631000件/30min9以双向60为基准磨削2530长至尺寸要求,保证四轴颈圆柱度要求1431外圆模砂轮千分尺、游标卡尺12min10按图纸要求检查Robotics and Computer-Integrated Manufacturing 21 (2005) 368378Locating completeness evaluation and revision in fixture planH. Song?, Y. RongCAM Lab, Department of Mechanical Engineering, Worcester Polytechnic Institute, 100 Institute Rd, Worcester, MA 01609, USAReceived 14 September 2004; received in revised form 9 November 2004; accepted 10 November 2004AbstractGeometry constraint is one of the most important considerations in fixture design. Analytical formulation of deterministiclocation has been well developed. However, how to analyze and revise a non-deterministic locating scheme during the process ofactual fixture design practice has not been thoroughly studied. In this paper, a methodology to characterize fixturing systemsgeometry constraint status with focus on under-constraint is proposed. An under-constraint status, if it exists, can be recognizedwith given locating scheme. All un-constrained motions of a workpiece in an under-constraint status can be automatically identified.This assists the designer to improve deficit locating scheme and provides guidelines for revision to eventually achieve deterministiclocating.r 2005 Elsevier Ltd. All rights reserved.Keywords: Fixture design; Geometry constraint; Deterministic locating; Under-constrained; Over-constrained1. IntroductionA fixture is a mechanism used in manufacturing operations to hold a workpiece firmly in position. Being a crucialstep in process planning for machining parts, fixture design needs to ensure the positional accuracy and dimensionalaccuracy of a workpiece. In general, 3-2-1 principle is the most widely used guiding principle for developing a locationscheme. V-block and pin-hole locating principles are also commonly used.A location scheme for a machining fixture must satisfy a number of requirements. The most basic requirement is thatit must provide deterministic location for the workpiece 1. This notion states that a locator scheme producesdeterministic location when the workpiece cannot move without losing contact with at least one locator. This has beenone of the most fundamental guidelines for fixture design and studied by many researchers. Concerning geometryconstraint status, a workpiece under any locating scheme falls into one of the following three categories:1. Well-constrained (deterministic): The workpiece is mated at a unique position when six locators are made to contactthe workpiece surface.2. Under-constrained: The six degrees of freedom of workpiece are not fully constrained.3. Over-constrained: The six degrees of freedom of workpiece are constrained by more than six locators.In 1985, Asada and By 1 proposed full rank Jacobian matrix of constraint equations as a criterion and formed thebasis of analytical investigations for deterministic locating that followed. Chou et al. 2 formulated the deterministiclocating problem using screw theory in 1989. It is concluded that the locating wrenches matrix needs to be full rank toachieve deterministic location. This method has been adopted by numerous studies as well. Wang et al. 3 consideredARTICLE IN PRESS front matter r 2005 Elsevier Ltd. All rights reserved.doi:10.1016/j.rcim.2004.11.012?Corresponding author. Tel.: +15088316092; fax: +15088316412.E-mail address: hsongwpi.edu (H. Song).locatorworkpiece contact area effects instead of applying point contact. They introduced a contact matrix andpointed out that two contact bodies should not have equal but opposite curvature at contacting point. Carlson 4suggested that a linear approximation may not be sufficient for some applications such as non-prismatic surfaces ornon-small relative errors. He proposed a second-order Taylor expansion which also takes locator error interaction intoaccount. Marin and Ferreira 5 applied Chous formulation on 3-2-1 location and formulated several easy-to-followplanning rules. Despite the numerous analytical studies on deterministic location, less attention was paid to analyzenon-deterministic location.In the Asada and Bys formulation, they assumed frictionless and point contact between fixturing elements andworkpiece. The desired location is q*, at which a workpiece is to be positioned and piecewisely differentiable surfacefunction is gi(as shown in Fig. 1).The surface function is defined as giq? 0: To be deterministic, there should be a unique solution for the followingequation set for all locators.giq 0;i 1;2;.;n,(1)where n is the number of locators and q x0;y0;z0;y0;f0;c0? represents the position and orientation of theworkpiece.Only considering the vicinity of desired location q?; where q q? Dq; Asada and By showed thatgiq giq? hiDq,(2)where hiis the Jacobian matrix of geometry functions, as shown by the matrix in Eq. (3). The deterministic locatingrequirement can be satisfied if the Jacobian matrix has full rank, which makes the Eq. (2) to have only one solutionq q?:rankqg1qx0qg1qy0qg1qz0qg1qy0qg1qf0qg1qc0:qgiqx0qgiqy0qgiqz0qgiqy0qgiqf0qgiqc0:qgnqx0qgnqy0qgnqz0qgnqy0qgnqf0qgnqc026666666664377777777758:9=; 6.(3)Upon given a 3-2-1 locating scheme, the rank of a Jacobian matrix for constraint equations tells the constraint statusas shown in Table 1. If the rank is less than six, the workpiece is under-constrained, i.e., there exists at least one freemotion of the workpiece that is not constrained by locators. If the matrix has full rank but the locating scheme hasmore than six locators, the workpiece is over-constrained, which indicates there exists at least one locator such that itcan be removed without affecting the geometry constrain status of the workpiece.For locating a model other than 3-2-1, datum frame can be established to extract equivalent locating points. Hu 6has developed a systematic approach for this purpose. Hence, this criterion can be applied to all locating schemes.ARTICLE IN PRESSX Y Z O X Y Z O (x0,y0,z0) gi UCS WCS Workpiece Fig. 1. Fixturing system model.H. Song, Y. Rong / Robotics and Computer-Integrated Manufacturing 21 (2005) 368378369Kang et al. 7 followed these methods and implemented them to develop a geometry constraint analysis module intheir automated computer-aided fixture design verification system. Their CAFDV system can calculate the Jacobianmatrix and its rank to determine locating completeness. It can also analyze the workpiece displacement and sensitivityto locating error.Xiong et al. 8 presented an approach to check the rank of locating matrix WL(see Appendix). They also intro-duced left/right generalized inverse of the locating matrix to analyze the geometric errors of workpiece. It hasbeen shown that the position and orientation errors DX of the workpiece and the position errors Dr of locators arerelated as follows:Well-constrained :DX WLDr,(4)Over-constrained :DX WTLWL?1WTLDr,(5)Under-constrained :DX WTLWLWTL?1Dr I6?6? WTLWLWTL?1WLl,(6)where l is an arbitrary vector.They further introduced several indexes derived from those matrixes to evaluate locator configurations, followed byoptimization through constrained nonlinear programming. Their analytical study, however, does not concern therevision of non-deterministic locating. Currently, there is no systematic study on how to deal with a fixture design thatfailed to provide deterministic location.2. Locating completeness evaluationIf deterministic location is not achieved by designed fixturing system, it is as important for designers to knowwhat the constraint status is and how to improve the design. If the fixturing system is over-constrained, informa-tion about the unnecessary locators is desired. While under-constrained occurs, the knowledge about all the un-constrained motions of a workpiece may guide designers to select additional locators and/or revise the locatingscheme more efficiently. A general strategy to characterize geometry constraint status of a locating scheme is describedin Fig. 2.In this paper, the rank of locating matrix is exerted to evaluate geometry constraint status (see Appendixfor derivation of locating matrix). The deterministic locating requires six locators that provide full rank locatingmatrix WL:As shown in Fig. 3, for given locator number n; locating normal vector ai;bi;ci? and locating position xi;yi;zi? foreach locator, i 1;2;.;n; the n ? 6 locating matrix can be determined as follows:WLa1b1c1c1y1? b1z1a1z1? c1x1b1x1? a1y1:aibiciciyi? biziaizi? cixibixi? aiyi:anbncncnyn? bnznanzn? cnxnbnxn? anyn2666666437777775.(7)When rankWL 6 and n 6; the workpiece is well-constrained.When rankWL 6 and n46; the workpiece is over-constrained. This means there are n ? 6 unnecessary locatorsin the locating scheme. The workpiece will be well-constrained without the presence of those n ? 6 locators. Themathematical representation for this status is that there are n ? 6 row vectors in locating matrix that can be expressedas linear combinations of the other six row vectors. The locators corresponding to that six row vectors consist oneARTICLE IN PRESSTable 1RankNumber of locatorsStatuso 6Under-constrained 6 6Well-constrained 646Over-constrainedH. Song, Y. Rong / Robotics and Computer-Integrated Manufacturing 21 (2005) 368378370locating scheme that provides deterministic location. The developed algorithm uses the following approach todetermine the unnecessary locators:1. Find all the combination of n ? 6 locators.2. For each combination, remove that n ? 6 locators from locating scheme.3. Recalculate the rank of locating matrix for the left six locators.4. If the rank remains unchanged, the removed n ? 6 locators are responsible for over-constrained status.This method may yield multi-solutions and require designer to determine which set of unnecessary locators shouldbe removed for the best locating performance.When rankWLo6; the workpiece is under-constrained.3. Algorithm development and implementationThe algorithm to be developed here will dedicate to provide information on un-constrained motions of theworkpiece in under-constrained status. Suppose there are n locators, the relationship between a workpieces position/ARTICLE IN PRESSFig. 2. Geometry constraint status characterization.X Z Y (a1,b1,c1) 2,b2,c2) (x1,y1,z1) (x2,y2,z2) (ai,bi,ci) (xi,yi,zi) (aFig. 3. A simplified locating scheme.H. Song, Y. Rong / Robotics and Computer-Integrated Manufacturing 21 (2005) 368378371orientation errors and locator errors can be expressed as follows:DX DxDyDzaxayaz2666666666437777777775w11:w1i:w1nw21:w2i:w2nw31:w3i:w3nw41:w4i:w4nw51:w5i:w5nw61:w6i:w6n2666666666437777777775?Dr1:Dri:Drn2666666437777775,(8)where Dx;Dy;Dz;ax;ay;azare displacement along x, y, z axis and rotation about x, y, z axis, respectively. Driisgeometric error of the ith locator. wijis defined by right generalized inverse of the locating matrix Wr WTLWLWTL?15.To identify all the un-constrained motions of the workpiece, V dxi;dyi;dzi;daxi;dayi;dazi? is introduced such thatV DX 0.(9)Since rankDXo6; there must exist non-zero V that satisfies Eq. (9). Each non-zero solution of V represents an un-constrained motion. Each term of V represents a component of that motion. For example, 0;0;0;3;0;0? says that therotation about x-axis is not constrained. 0;1;1;0;0;0? means that the workpiece can move along the direction given byvector 0;1;1?: There could be infinite solutions. The solution space, however, can be constructed by 6 ? rankWLbasic solutions. Following analysis is dedicated to find out the basic solutions.From Eqs. (8) and (9)VX dxDx dyDy dzDz daxDax dayDay dazDaz dxXni1w1iDri dyXni1w2iDri dzXni1w3iDri daxXni1w4iDri dayXni1w5iDri dazXni1w6iDriXni1Vw1i;w2i;w3i;w4i;w5i;w6i?TDri 0.10Eq. (10) holds for 8Driif and only if Eq. (11) is true for 8i1pipn:Vw1i;w2i;w3i;w4i;w5i;w6i?T 0.(11)Eq. (11) illustrates the dependency relationships among row vectors of Wr: In special cases, say, all w1jequal to zero,V has an obvious solution 1, 0, 0, 0, 0, 0, indicating displacement along the x-axis is not constrained. This is easy tounderstand because Dx 0 in this case, implying that the corresponding position error of the workpiece is notdependent of any locator errors. Hence, the associated motion is not constrained by locators. Moreover, a combinedmotion is not constrained if one of the elements in DX can be expressed as linear combination of other elements. Forinstance, 9w1ja0;w2ja0; w1j ?w2jfor 8j: In this scenario, the workpiece cannot move along x- or y-axis. However, itcan move along the diagonal line between x- and y-axis defined by vector 1, 1, 0.To find solutions for general cases, the following strategy was developed:1. Eliminate dependent row(s) from locating matrix. Let r rank WL; n number of locator. If ron; create a vectorin n ? r dimension space U u1:uj:un?rhi1pjpn ? r; 1pujpn: Select ujin the way that rankWL r still holds after setting all the terms of all the ujth row(s) equal to zero. Set r ? 6 modified locating matrixWLMa1b1c1c1y1? b1z1a1z1? c1x1b1x1? a1y1:aibiciciyi? biziaizi? cixibixi? aiyi:anbncncnyn? bnznanzn? cnxnbnxn? anyn2666666437777775r?6,where i 1;2;:;niauj:ARTICLE IN PRESSH. Song, Y. Rong / Robotics and Computer-Integrated Manufacturing 21 (2005) 3683783722. Compute the 6 ? n right generalized inverse of the modified locating matrixWr WTLMWLMWTLM?1w11:w1i:w1rw21:w2i:w2rw31:w3i:w3rw41:w4i:w4rw51:w5i:w5rw61:w6i:w6r26666666664377777777756?r3. Trim Wrdown to a r ? rfull rank matrix Wrm: r rankWLo6: Construct a 6 ? r dimension vector Q q1:qj:q6?rhi1pjp6 ? r; 1pqjpn: Select qjin the way that rankWr r still holds after setting all theterms of all the qjth row(s) equal to zero. Set r ? r modified inverse matrixWrmw11:w1i:w1r:wl1:wli:wlr:w61:w6i:w6r26666664377777756?6,where l 1;2;:;6 laqj:4. Normalize the free motion space. Suppose V V1;V2;V3;V4;V5;V6? is one of the basic solutions of Eq. (10) withall six terms undetermined. Select a term qkfrom vector Q1pkp6 ? r: SetVqk ?1;Vqj 0 j 1;2;:;6 ? r;jak;(5. Calculated undetermined terms of V: V is also a solution of Eq. (11). The r undetermined terms can be found asfollows.v1:vs:v62666666437777775wqk1:wqki:wqkr2666666437777775?w11:w1i:w1r:wl1:wli:wlr:w61:w6i:w6r2666666437777775?1,where s 1;2;:;6saqj;saqk;l 1;2;:;6 laqj:6. Repeat step 4 (select another term from Q) and step 5 until all 6 ? r basic solutions have been determined.Based on this algorithm, a C+ program was developed to identify the under-constrained status and un-constrained motions.Example 1. In a surface grinding operation, a workpiece is located on a fixture system as shown in Fig. 4. The normalvector and position of each locator are as follows:L1:0, 0, 10, 1, 3, 00,L2:0, 0, 10, 3, 3, 00,L3:0, 0, 10, 2, 1, 00,L4:0, 1, 00, 3, 0, 20,L5:0, 1, 00, 1, 0, 20.Consequently, the locating matrix is determined.WL0013?100013?300011?20010?203010?2012666666437777775.ARTICLE IN PRESSH. Song, Y. Rong / Robotics and Computer-Integrated Manufacturing 21 (2005) 368378373This locating system provides under-constrained positioning since rankWL 5o6: The program then calculatesthe right generalized inverse of the locating matrix.Wr000000:50:5?1?0:51:50:75?1:251:5000:250:25?0:5000:5?0:50000000:5?0:526666666643777777775.The first row is recognized as a dependent row because removal of this row does not affect rank of the matrix. Theother five rows are independent rows. A linear combination of the independent rows is found according therequirement in step 5 of the procedure for under-constrained status. The solution for this special case is obvious that allthe coefficients are zero. Hence, the un-constrained motion of workpiece can be determined as V ?1; 0; 0; 0; 0; 0?:This indicates that the workpiece can move along x direction. Based on this result, an additional locator should beemployed to constraint displacement of workpiece along x-axis.Example 2. Fig. 5 shows a knuckle with 3-2-1 locating system. The normal vector and position of each locator in thisinitial design are as follows:L1:0, 1, 00, 896, ?877, ?5150,L2:0, 1, 00, 1060, ?875, ?3780,L3:0, 1, 00, 1010, ?959, ?6120,L4:0.9955, ?0.0349, 0.0880, 977, ?902, ?6240,L5:0.9955, ?0.0349, 0.0880, 977, ?866, ?6240,L6:0.088, 0.017, ?0.9960, 1034, ?864, ?3590.The locating matrix of this configuration isWL010515:000:8960010378:001:0600010612:001:01000:9955?0:03490:0880?101:2445?707:26640:86380:9955?0:03490:0880?98:0728?707:26640:82800:08800:0170?0:9960866:6257998:24660:093626666666643777777775,rankWL 5o6 reveals that the workpiece is under-constrained. It is found that one of the first five rows can beremoved without varying the rank of locating matrix. Suppose the first row, i.e., locator L1is removed from WL; theARTICLE IN PRESSXZYL3L4L5L2L1Fig. 4. Under-constrained locating scheme.H. Song, Y. Rong / Robotics and Computer-Integrated Manufacturing 21 (2005) 368378374modified locating matrix turns intoWLM010378:001:0600010612:001:01000:9955?0:03490:0880?101:2445?707:26640:86380:9955?0:03490:0880?98:0728?707:26640:82800:08800:0170?0:996866:6257998:24660:09362666666437777775.The right generalized inverse of the modified locating matrix isWr1:8768?1:8607?20:666521:37160:49953:0551?2:0551?32:444832:44480?1:09561:086212:0648?12:4764?0:2916?0:00440:00440:0061?0:006100:0025?0:00250:0065?0:00690:0007?0:00040:00040:0284?0:0284026666666643777777775.The program checked the dependent row and found every row is dependent on other five rows. Without losinggenerality, the first row is regarded as dependent row. The 5 ? 5 modified inverse matrix isWrm3:0551?2:0551?32:444832:44480?1:09561:086212:0648?12:4764?0:2916?0:00440:00440:0061?0:006100:0025?0:00250:0065?0:00690:0007?0:00040:00040:0284?0:028402666666437777775.The undetermined solution is V ?1; v2; v3; v4; v5; v6?:To calculate the five undetermined terms of V according to step 5,1:8768?1:8607?20:666521:37160:499526666666643777777775T?3:0551?2:0551?32:444832:44480?1:09561:086212:0648?12:4764?0:2916?0:00440:00440:0061?0:006100:0025?0:00250:0065?0:00690:0007?0:00040:00040:0284?0:0284026666666643777777775?1 0; ?1:713; ?0:0432; ?0:0706; 0:04?.Substituting this result into the undetermined solution yields V ?1;0; ?1:713; ?0:0432; ?0:0706; 0:04?ARTICLE IN PRESSFig. 5. Knuckle 610 (modified from real design).H. Song, Y. Rong / Robotics and Computer-Integrated Manufacturing 21 (2005) 368378375This vector represents a free motion defined by the combination of a displacement along ?1, 0, ?1.713 directioncombined and a rotation about ?0.0432, ?0.0706, 0.04. To revise this locating configuration, another locator shouldbe added to constrain this free motion of the workpiece, assuming locator L1was removed in step 1. The program canalso calculate the free motions of the workpiece if a locator other than L1was removed in step 1. This provides morerevision options for designer.4. SummaryDeterministic location is an important requirement for fixture locating scheme design. Analytical criterion fordeterministic status has been well established. To further study non-deterministic status, an algorithm for checking thegeometry constraint status has been developed. This algorithm can identify an under-constrained status and indicatethe un-constrained motions of workpiece. It can also recognize an over-constrained status and unnecessary locators.The output information can assist designer to analyze and improve an existing locating scheme.Appendix. Locating matrixConsider a general workpiece as shown in Fig. 6. Choose reference frame fWg fixed to the workpiece. Let fGg andfLig be the global frame and the ith locator frame fixed relative to it. We haveFiXw;Hw;rwi fiXli;Hli;rli,(12)where Xw2 3?1and Hw2 3?1(Xli2 3?1and Hli2 3?1) are the position and orientation of the workpiece(the ith locator) in the global frame fGg; rwi2 3?1(rli2 3?1) is the position of the ith contact point between theworkpiece and the ith locator in the workpiece frame fWg (the ith locator frame fLig).Assume that DXw2 3?1(DHw2 3?1) and Drwi2 3?1are the deviations of the position Xw2 3?1(orientationHw2 3?1) of the workpiece and the position of the ith contact point rwi2 3?1; respectively. Then we have the actualcontact on the wor
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